Abstract. It is well-known that data abstraction badly
coexists with pattern matching. Pattern matching is applicable in the domain
with "transparent" structure of symbolical data while the traditional data
abstraction supposes hiding data from the user. In this paper, it is shown
how it is possible to provide data abstraction at reception of all
completeness of convenience of it by simple means within the framework of
the system of symbolic manipulations based on pattern matching. At that the
problem is not put to hide abstract data from the programmer completely.

In our case data abstraction is based on possibility of
obtaining of values of functions, being inversed to functions-constructors,
that in turn is based on possibility of dynamic computation of patterns. At
that multilevel computations are widely used, providing, in particular, used
way of pattern matching.

The examples of data abstraction given in this paper are
based on the subsystem of algebraic computations that has been built in the
system of symbolic manipulations.